The Development of Multi-Point Laser Doppler Anemometry (MPLDA): A New Method to
Estimate Fluid Flow Statistics
by
J.M. Coupland(1) and N.J. Lawson(2)
(1)
Loughborough University, Loughborough LE11 3TU UK
E-mail: j.m.coupland@lboro.ac.uk
(2)
Cranfield University, Cranfield MK43 0AL UK
E-mail: n.lawson@cranfield.ac.uk
ABSTRACT
In this paper we describe a method to measure fluid flow fields that we call Multi-Point Laser Doppler Anemometry
(MPLDA). Like Doppler Global Velocimetry (DGV) and single point Laser Doppler Anemometry (LDA), the
technique derives information from the Doppler shift observed when light is scattered from a moving particle and
exploits the advantages of these techniques. The method retains the elegant simplicity of DGV, but uses coherent
heterodyne detection as in LDA rather than applying an absorption edge to demodulate the Doppler signal (as in DGV).
This makes MPLDA suitable for the measurement of flow fields throughout the velocity range. In contrast with pulsed
laser imaging techniques, such as Particle Image Velocimetry (PIV) and its derivatives, MPLDA does not require
individual seeding particles to be resolved as is the case with LDA and DGV. We believe that this makes MPLDA
unique in its ability to gain whole field measurements in large scale, low speed wind tunnel facilities.
In essence MPLDA utilises a streak camera and coherent detection to record a short segments of the Doppler signals
collected from many points within a seeded flow field. The streak image is then analysed to estimate the Doppler
frequency at each point in the flow. In our original studies we used reflection from a galvanometer mirror to implement
streak imaging. Using this technology we were able to prove the principles of MPLDA by measuring the surface
velocity of a spinning disk. In this case the disk velocity was low (1/20 rev/sec) and consequently the measured Doppler
frequencies were in the range of 0-10kHz. These initial results clearly demonstrated the potential of MPLDA, however,
the scale and speed of the experiment are several orders of magnitude less than that which would be expected in a wind
tunnel. In addition the reference beam necessary for coherent detection did not include a frequency shift and as such the
measurements were subject to directional ambiguity.
More recently we have conducted investigations into the use of electronic vacuum tube technology as a means to
implement the streak imaging requirement of MPLDA. A streak tube of this kind is similar in principle to an image
intensifier and uses deflection plates to displace electrons en route to an output phosphor screen. In this way pico
second resolution is possible. In what follows, a streak tube in conjunction with a Peltier cooled CCD camera is used to
provide a flexible MPLDA streak system for both low and high speed wind tunnel facilities. We demonstrate the use of
this system as a means to measure the velocity of spray particles within the measurement volume of a basic, single
component, LDA system.
1
INTRODUCTION
Non-intrusive optical flow measurement techniques are vitally important in the study of fluid flow phenomena both to
provide new insight into flow behaviour and increasingly, as a means to validate computational models. Single-point
velocity measurements are commonly made using Laser Doppler Anemometry (LDA) (Durrani and Greated, 1977)
while Particle Image Velocimetry (PIV) (Adrian 1991) is now an established method to make planar, two -component
velocity measurements and stereoscopic (Lawson and Wu, 1999) and holographic techniques (Coupland and Halliwell,
1997) can be employed to make three-component measurements. More recently Doppler Global Velocimetry (DGV)
has been demonstrated by Komine and Brosnan (1991) and has been refined and extended by Meyers (1995) and others
to make planar three-component measurements in practice.
In order to perform quantitative comparisons with computational models, the choice of experimental technique is
strongly influenced by the ability to collect sufficient data to characteris e a given flow in a reasonable time. In this
respect, the elegant simplicity of DGV is very appealing, particularly when three-component measurements are desired.
The technique is also more appropriate to large-scale air flows than PIV since it is not necessary to identify individual
particles in the flow and for this reason the increased scattering efficiency afforded by a fine seeding mist or smoke,
rather than large (and heavy) particles, can be exploited. A major limitation of DGV remains however. Although the
technique is relatively straightforward to implement in the study of high-speed (supersonic) flows, the need for a well
stabilised laser source and SNR limitations of the sensor restrict the resolution of the technique to a few metres per
second in practice (McKenzie 1996).
We have recently demonstrated a technique that is applicable throughout the velocity range 0 - 100km/s (Coupland
2000). The technique that we now call Multi-Point Laser Doppler Anemometry (MPLDA) retains much of the
simplicity of DGV and derives velocity information from the Doppler shift associated with light scattered from a laser
illuminated fluid flow. However, a stabilised source is not necessary since we implement coherent detection using a
streak camera. In the following paper, we introduce MPLDA and describe our initial proof of principle experiments
using a rotating mirror streak camera that allowed us to measure flows at a relatively small scale and small velocity. We
then discuss a more robust and flexible implementation of MPLDA using a vacuum tube streak camera, which can be
used for large scale studies throughout the velocity range.
THE MPLDA METHOD
The most general MPLDA geometry for three-component measurement of flow structure within a wind tunnel section is
shown in figure 1. In essence, this geometry is similar to that proposed by Meyers (1995) for three-component,
transonic DGV studies and consists of three CCD cameras (I,II and III). Cameras I and II view the flow from opposite
directions whilst the third camera, III has an orthogonal view such that the optical axes of all the cameras lie in a single
plane. The flow is illuminated with coherent light that propagates in a direction orthogonal to this plane. In traditional
DGV this is usually in the form of a light sheet, however, for reasons which will become apparent, a set of parallel (not
necessarily coplanar) propagating laser beams are preferred here.
Camera III
Parallel laser
beam
illumination
Camera I
Flow
Camera II
Fig. 1. MPLDA geometry
2
It is well known that if a particle moving with velocity, v, is illuminated by a laser beam, the Doppler shift, ∆ν ,
observed in the scattered light is given by,
∆ν =
(
)
n kˆ s − kˆ i .v
λ
(1.)
where n is the refractive index of the ambient fluid, λ, is the wavelength and, k̂ s and k̂ i , are unit vectors in the
direction of propagation of the scattered and illuminating fields respectively. Thus the Doppler shift is directly
proportional to the velocity in the direction of the sensitivity vector, s , defined by, s = n kˆ s − kˆ i λ . With reference to
(
)
figure 1, it can be seen that at the point where the optical axes cross, s I , s II and s III corresponding to the sensitivity
vectors of each camera, are mutually orthogonal. Thus the Doppler shift in the light collected by each camera from this
point is proportional to an orthogonal component of the fluid velocity.
Using the geometry discussed above, with v=1m/s, λ=514nm and n=1, the Doppler shift is found to be approximately
3MHz and represents a frequency change of about 1 part in 2×108 . In practical, DGV instrumentation the Doppler shift
is measured by comparing the intensity of an image recorded through an Iodine cell with that recorded without such a
filter. The absorption edge of Iodine vapour has a bandwidth of approximately 400Mz and a gradient such that a 1%
change in intensity transmittance is observed for a 10MHz excursion which corresponds to a velocity resolution of
about 3.6m/s using the geometry of figure 1 at λ=514nm. It is clear that in order to achieve a measurement resolution
approaching this value, the wavelength of the laser and the Iodine absorption line must be mutually stable. Although
Roehle and Schodl (1994) have demonstrated a system of this kind, practical problems of camera alignment and
detector noise remain. For this reason, it is unlikely that DGV using Iodine demodulation methods will find widespread
application outside of transonic or supersonic flow studies.
Since it is the Doppler shift rather than the absolute frequency that is of interest, mixing the scattered light with a
coherent reference wave provides a demodulation method which is insensitive to small changes in the source frequency.
This method is the basis of single point laser Doppler anemometry (LDA) first proposed by Yeh and Cummins (1964)
and is also used in Doppler Lidar systems for the remote measurement of atmospheric turbulence (Intriei et. al., 1990)
In order to employ coherent detection in simultaneous, whole field measurements, however, it is necessary to have an
imaging detector of high bandwidth to record the temporal information necessary to resolve the Doppler shift.
The basis of MPLDA is to use streak cameras to record the Doppler signal (Doppler burst) scattered from points along
the length of the laser beams. In essence a streak camera provides both spatial and temporal information by translating
the time varying image across a stationary CCD detector. In this way, the intensity of the light scattered from a laser
beam can be found as a function of time and if the scattered light is mixed with a reference wave then a periodic
fluctuation in intensity is observed at the Doppler frequency. This is illustrated in figure 2.
Final
position
Laser beams’ initial
position
…,etc
t
t+∆t t
t+∆t t
Fig. 2. Streak image
3
t+∆t
In this case the translation effected by the streak camera is in the horizontal direction and has been truncated such that a
short burst of the time history can be seen for several laser beams that appear as vertical lines. Fourier transformation of
each burst is then used to recover the mean Doppler frequency. The major advantage of MPLDA over PIV is that it is
not necessary to identify individual particles in the image to make flow measurements. In conventional PIV the
superposition of particle images results in a speckle pattern that is subject to de-correlation in the relatively long periods
between exposures necessary to achieve a measurable displacement. For this reason PIV is inappropriate for many wind
tunnel studies where the scale would necessitate seeding with prohibitively large and heavy particles to ensure adequate
particle image exposures. In contrast MPLDA has the potential to work well with a fine seeding mist or smoke particles
that are often used for flow visualisation in these facilities.
PRELIMINARY WORK
In our original work we used reflection from a galvanometer mirror to streak the image across a progressive scan CCD
sensor (Coupland 2000). Initially, the configuration was used to measure the tangential velocity along a line through the
centre of spinning disk as shown in figure 3.
Coherent
reference
beam
Laser beam
out of page
Cylindrical
lens
CCD camera
Rotating
mirror
Spinning
disk
Fig. 3. Spinning disk configuration
The disk surface was illuminated at grazing incidence with a single laser beam of wavelength λ = 532 nm and
approximately 0.25mm in diameter. The disk was driven by a signal generator at an angular velocity of 0.31 rad/sec
(1/20 rev/sec) and the galvanometer mirror was driven with a triangular waveform at the camera frame rate of 25Hz.
The amplitude was adjusted such that the angular excursion of the mirror was sufficient to produce a full width streak
image 768 pixels in length giving an effective sampling rate of 38.4kHz. In this way a single streak was recorded in
each frame. Figure 4 shows a typical streak image.
Fig. 4. Spinning disk streak image
4
Demodulation of this image was accomplished by one-dimensional power spectrum of each line in the image and
scaling according to the effective sampling rate and the results are shown in figure 5. Finally, the Doppler shift was
calculated by finding the positions of the dominant peaks in each line of figure 5 and from consideration of the
geometry the magnitute of the disk velocity was calculated at each point using equation 1. Figure 6 shows the measured
velocity along the laser beam (crosses) and its theoretical value (solid line). The small overestimate in velocity is
attributed to an inaccuracy in the measurement geometry.
-3
3
-15
2.5
Velocity s-component m/s
-10
Radial distance mm
x 10
-5
0
2
1.5
1
5
0.5
10
1
2
3
4
5
Doppler frequency kHz
6
0
-15
7
Fig. 5. Demodulated power spectra
-10
-5
0
5
Radial distance mm
10
15
Fig.6. Measured (crosses) and theoretical
(solid line) velocity
Although these results were encouraging, it is noted that the diameter of the disk (20mm) and the range of measured
velocity (< 3mm/s) are both very small and are several orders of magnitude less than that expected in a practical flow
measurement situation. In addition, it is noted that only the magnitude of the velocity has been measured and, like LDA,
a frequency shift in the reference beam is necessary to resolve directional ambiguity. On the basis of these results it was
decided to build new instrumentation capable of large scale work that can be used to measure flow velocities in a range
typical of a subsonic wind tunnel (0.1-10m/s). This is described in the following section.
STREAK TUBE INSTRUMENTATION
Inspection of equation 1 shows that the maximum Doppler shift occurs in back-scatter geometry ( kˆ s = −kˆ s ) and at a
velocity of 10m/s and wavelength of 532nm this corresponds to approximately 38MHz. Although it is possible to
design a mechanical streak camera using rotating mirrors for example, that is capable of recording a signal of this
frequency, it would require expensive specialist mechanics. A more flexible and cost effective approach is to use a
streak tube based on vacuum tube technology (Johnson et. al 1980). This technology has been developed to investigate
ultra-fast phenomena and is capable of pico-second resolution and with effectively no lower limit. Streak tube
technology can therefore be configured to measure flow velocity from zero to over 100km/s!
Figure 7 shows a schematic of our streak camera. The streak tube used is a photochron 5 tube from Photek Ltd. The
tube consists of a blue/green sensitive S25 photocathode, an image intensifier section with x-y deflection plates, and a
fast response phosphor (1ms). The output image is relayed to a 12bit 1280x1024 Vosskuhler COOL-1300Q CCD array.
With this arrangement we have shown that the streak camera is capable of recording events with a bandwidth in excess
of 1GHz and an output frame rate of up to 12fps.
5
Relay lens
Imaging lens
Photocathode
Cooled CCD
Phosphor
screen
Deflection
plates
Fig. 7. Schematic of a vacuum tube streak camera
Due to late delivery of the streak tube we can only report our initial tests of the streak camera system. In these tests the
streak camera was used to image the probe volume of a basic cross-beam LDA system as shown in figure 8. The LDA
used a rotating diffraction grating to give a frequency shift of 1.4MHz. In this configuration the width of the probe
volume and fringe frequency were approximately 125µm and 10µm respectfully. The LDA operated at a wavelength of
532nm using Coherent Verdi laser at 500mW.
Rotating diffraction
grating
Streak camera
500mW laser beam
Fig. 8. Streak recording of cross-beam LDA
In these studies a water spray with an estimated drop size of 50µm was directed through the flow volume. Figure 9a)-c)
show the streak images obtained approximately 1m from the probe volume using an F#1.4 16mm lens. Each streak is
10µs duration. Figure 9a) shows a spray particle travelling nominally parallel to the cross-beam fringes and shows the
1.4MHz reference frequency. Figures 9b) and c) show spray directed toward and away from the sensitivity vector
respectively. It can be deduced that the spray velocity is approximately 9m/s.
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Fig. 9. Streak recording of cross-beam LDA with spray directed;
a) parallel to fringes b) along the sensitivity vector c) opposite to the sensitivity vector
CONCLUSION
It is clear from the results presented in this paper that it is possible to construct an MPLDA system utilising streak
imaging to record Doppler bursts from many points along the path of one or more laser beams. Mechanical systems
using rotating mirrors can be used to implement streak imaging but electronic streak tube technology provides a more
robust solution and a specification that makes it applicable to the measurement flow fields throughout the velocity
range. Thus with picosecond streak periods, it may be possible to measure velocities up to 100 km/s. In the initial tests
presented here, we have proved the MPLDA principle by measuring surface velocity of a low-speed inclined disk and
we have also demonstrated the new streak tube technique by measuring a droplet spay at a more typical flow velocity
by imaging a cross-beam LDA configuration through the streak tube camera. Our next objective is to build a full scale
streak tube MPLDA system for use in a medium scale, sub-sonic wind tunnel.
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